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Gen Nakamura

Publications and source records attributed to Gen Nakamura.

At least 55 records · Page 3Linked to original sources
arXiv2017

Boundary determination of the Lamé moduli for the isotropic elasticity system

We consider the inverse boundary value problem of determining the Lamé moduli of an isotropic, static elasticity equations of system at the boundary from the localized Dirichlet-to-Neumann map. Assuming appropriate local regularity assumptions as weak as possible on the Lamé moduli and on the boundary, we give explicit pointwise reconstruction formulae of the Lamé moduli and their higher order derivatives at the boundary from the localized Dirichlet-to-Neumann map.

math.AP↗
arXiv2017

Convergence of Lebenberg-Marquard method for the Inverse Problem with an Interior Measurement

The convergence of Levenberg-Marquard method is discussed for the inverse problem to reconstruct the storage modulus and loss modulus for the so called scalar model by single interior measurement. The scalar model is the most simplest model for data analysis used as the modeling partial differential equation in the diagnosing modality called the magnetic resonance elastography which is used to diagnose for instance lever cancer. The convergence of the method is proved by showing that the measurement map which maps the above unknown moduli to the measured data satisfies the so called the tangential cone condition. The argument of the proof is quite general and in principle can be applied to any similar inverse problem to reconstruct the unknown coefficients of the model equation given as a partial differential equation of divergence form by one single interior measurement. The performance of the method is numerically tested for the two layered picewise homogneneous scalar model in a rectangular domain.

math.NA↗
arXiv2017

Stationary viscoelastic wave fields generated by scalar wave functions

The usual Helmholtz decomposition gives a decomposition of any vector valued function into a sum of gradient of a scalar function and rotation of a vector valued function under some mild condition. In this paper we show that the vector valued function of the second term i.e. the divergence free part of this decomposition can be further decomposed into a sum of a vector valued function polarized in one component and the rotation of a vector valued function also polarized in the same component. Hence the divergence free part only depends on two scalar functions. Further we show the so called completeness of representation associated to this decomposition for the stationary wave field of a homogeneous, isotropic viscoelastic medium. That is by applying this decomposition to this wave field, we can show that each of these three scalar functions satisfies a Helmholtz equation. Our completeness of representation is useful for solving boundary value problem in a cylindrical domain for several partial differential equations of systems in mathematical physics such as stationary isotropic homogeneous elastic/viscoelastic equations of system and stationary isotropic homogeneous Maxwell equations of system. As an example, by using this completeness of representation, we give the solution formula for torsional deformation of a pendulum of cylindrical shaped homogeneous isotropic viscoelastic medium.

math.AP↗
arXiv2017

Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $Ω$ which is a bounded domain consisting of a finite number of bounded subdomains $D_α$, with each $D_α$ a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an ansiotropic elastic medium. Assuming the $D_α$ are known and Lipschitz, we are concerned with the uniqueness in the inverse boundary value problem of identifying the anisotropic elasticity tensor on $Ω$ from a localized Dirichlet to Neumann map given on a part of the boundary $\partial D_{α_0}\cap\partialΩ$ of $\partialΩ$ for a single $α_0$, where $\partial D_{α_0}$ denotes the boundary of $ D_{α_0}$. If we can connect each $D_α$ to $D_{α_0}$ by a chain of $\{D_{α_i}\}_{i=1}^n$ such that interfaces between adjacent regions contain a curved portion, we obtain global uniqueness for this inverse boundary value problem. If the $D_α$ are not known but are subanalytic subsets of $\mathbb{R}^3$ with curved boundaries, then we also obtain global uniqueness.

math.AP↗
arXiv2017

Reconstruction of Lame moduli and density at the boundary enabling directional elastic wavefield decomposition

We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann map. More precisely, using the full symbol of the transformed Dirichlet-to-Neumann map viewed as a semiclassical pseudodifferential operator, we give an explicit reconstruction of both Lamé parameters and the density, as well as their derivatives, at the boundary. We also show how this boundary reconstruction leads to a decomposition of incoming and outgoing waves.

math.AP↗
arXiv2015

Reconstruction of an unknown cavity with Robin boundary condition inside a heat conductor

Active thermography is a non-destructive testing technique to detect the internal structure of a heat conductor, which is widely applied in industrial engineering. In this paper, we consider the problem of identifying an unknown cavity with Robin boundary condition inside a heat conductor from boundary measurements. To set up the inverse problem mathematically, we first state the corresponding forward problem and show its well-posedness in an anisotropic Sobolev space by the integral equation method. Then, taking the Neumann-to-Dirichlet map as mathematically idealized measured data for the active thermography, we present a linear sampling method for reconstructing the unknown Robin-type cavity and give its mathematical justification by using the layer potential argument. In addition, we analyze the indicator function used in this method and show its pointwise asymptotic behavior by investigating the reflected solution of the fundamental solution. From our asymptotic analysis, we can establish a pointwise reconstruction scheme for the boundary of the cavity, and can also know the distance to the unknown cavity as we probe it from its inside.

math-ph↗
arXiv2015

Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain

In this paper we establish the uniform estimates of strong solutions with respect to the Mach number and the dielectric constant to the full compressible Navier-Stokes-Maxwell system in a bounded domain. Based on these uniform estimates, we obtain the convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations for well-prepared data.

math.AP↗
arXiv2014

Carleman estimate and its application for anomalous slow diffusion equation

A Carleman estimate and the unique continuation of solutions for an anomalous diffusion equation with fractional time derivative of order $0<α<1$ are given. The estimate is derived via some subelliptic estimate for an operator associated to the anomalous diffusion equation using calculus of pseudo-differential operators.

math.AP↗
arXiv2013

Window effect in the power spectrum analysis of a galaxy redshift survey

We investigate the effect of the window function on the multipole power spectrum in two different ways. First, we consider the convolved power spectrum including the window effect, which is obtained by following the familiar (FKP) method developed by Feldman, Kaiser and Peacock. We show how the convolved multipole power spectrum is related to the original power spectrum, using the multipole moments of the window function. Second, we investigate the deconvolved power spectrum, which is obtained by using the Fourier deconvolution theorem. In the second approach, we measure the multipole power spectrum deconvolved from the window effect. We demonstrate how to deal with the window effect in these two approaches, applying them to the Sloan Digital Sky Survey (SDSS) luminous red galaxy (LRG) sample.

astro-ph.CO↗
arXiv2013

Conditional Stability for Single Interior Measurement

An inverse problem to identify unknown coefficients of a partial differential equation by a single interior measurement is considered. The equation considered in this paper is a strongly elliptic second order scalar equation which can have complex coefficients in a bounded domain with $C^2$ boundary and single interior measurement means that we know a given solution of the equation in this domain. The equation includes some model equations arising from acoustics, viscoelasticity and hydrology. We assume that the coefficients are piecewise analytic. Our major result is the local Hölder stability estimate for identifying the unknown coefficients. If the unknown coefficients is a complex coefficient in the principal part of the equation, we assumed a condition which we named admissibility assumption for the real part and imaginary part of the difference of the two complex coefficients. This admissibility assumption is automatically satisfied if the complex coefficients are real valued. For identifying either the real coefficient in the principal part or the coefficient of the 0-th order of the equation, the major result implies the global uniqueness for the identification.

math.AP↗
arXiv2012

Quantum Larmor radiation from a moving charge in an electromagnetic plane wave background

We extend our previous work [Phys. Rev. D83 045030 (2011)], which investigated the first-order quantum effect in the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field. Specifically, we investigate the quantum Larmor radiation from a moving charge in a monochromatic electromagnetic plane wave background based on the scalar quantum electrodynamics at the lowest order of the perturbation theory. Using the in-in formalism, we derive the theoretical formula of the total radiation energy from a charged particle in the initial states being at rest and being in a relativistic motion. Expanding the theoretical formula in terms of the Planck constant \hbar, we obtain the first-order quantum effect on the Larmor radiation. The quantum effect generally suppresses the total radiation energy compared with the prediction of the classical Larmor formula, which is a contrast to the previous work. The reason is explained by the fact that the radiation from a moving charge in a monochromatic electromagnetic plane wave is expressed in terms of the inelastic collisions between an electron and photons of the background electromagnetic waves.

hep-th↗
arXiv2012

Linear sampling method for identifying cavities in a heat conductor

We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a freedom to choose the time variable, which suggests that we have more data than the linear sampling methods for the inverse boundary value problem associated with EIT and inverse scattering problem with near field data.

math-ph↗
arXiv2011

First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field

First-order quantum correction to the Larmor radiation is investigated on the basis of the scalar QED on a homogeneous background of time-dependent electric field, which is a generalization of a recent work by Higuchi and Walker so as to be extended for an accelerated charged particle in a relativistic motion. We obtain a simple approximate formula for the quantum correction in the limit of the relativistic motion when the direction of the particle motion is parallel to that of the electric field.

hep-th↗
arXiv2011

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them manifolds of discontinuities. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. The both gradient estimates are independent of the distances between manifolds of discontinuities.

math.AP↗
arXiv2011

Quantum Larmor radiation in conformally flat universe

We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics (SQED). A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the SQED. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e^2\hbar is determined by a non-local integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D80 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a non-relativistic motion in a homogeneous electric field.

gr-qc↗
arXiv2010

Constraint on the cosmological f(R) model from the multipole power spectrum of the SDSS luminous red galaxy sample and prospects for a future redshift survey

A constraint on the viable f(R) model is investigated by confronting theoretical predictions with the multipole power spectrum of the luminous red galaxy sample of the Sloan Digital Sky survey data release 7. We obtain a constraint on the Compton wavelength parameter of the f(R) model on the scales of cosmological large-scale structure. A prospect of constraining the Compton wavelength parameter with a future redshift survey is also investigated. The usefulness of the redshift-space distortion for testing the gravity theory on cosmological scales is demonstrated.

astro-ph.CO↗